Recently, the use of femtosecond laser direct writing to produce optical devices inside transparent materials has been growing considerably. Tightly focused femtosecond laser pulses can induce nonlinear absorption within the focal volume and permanently modify the index of refraction of the material, as discussed in the following papers: T. Tamaki, W. Watanabe, H. Nagai, M. Yoshida, J. Nishii, and K. Itoh, Opt. Express 14, 6971-6980 (2006); and A. M. Streltsov and N. F. Borrelli, J. Opt. Soc. Am. B 19, 2496-2504 (2002). Although the mechanism responsible for refractive index increase by ultrashort laser pulses is not fully understood, researchers have fabricated various optical devices inside transparent materials with this direct writing method such as waveguides, gratings and diffractive optical elements (DOEs). Examples are discussed in the following papers, which are hereby incorporated by reference along with all other references cited herein:    A. M. Streltsov and N. F. Borrelli, J. Opt. Soc. Am. B 19, 2496-2504 (2002).    R. Osellame, S. Taccheo, M. Mariangoni, R. Ramponi, P. Laporta, D. Polli, S. De Silvestri, and G. Cerullo, J. Opt. Soc. Am. B 20, 1559-1567 (2003).    N. Takeshima, Y. Narita, S. Tanaka, Y. Kuroiwa, and K. Hirao, Opt. Lett. 30, 352-354 (2005).    W. Watanabe, D. Kuroda, K. Itoh, and J. Nishii, Opt. Express 10, 978-983 (2002).    E. Bricchi, J. D. Mills, P. G. Kazansky, B. G. Klappauf, and J. J. Baumberg, Opt. Lett. 27, 2200-2202 (2002).    K. Yamada, W. Watanabe, Y. Li, K. Itoh, and J. Nishii, Opt. Lett. 29, 1846-1848 (2004).
In recent years, the development of fabrication techniques for DOEs has accelerated because DOEs can perform many optical functions like lenses, gratings, optical signal processors, beam splitters, and wavelength (de)multiplexers. Fabrication of DOEs requires high-resolution techniques such as lithography. Femtosecond laser direct writing offers advantages as compared to other techniques such as volume writing, precision, speed, simplicity, and flexibility. In particular, this method of fabrication can be applied for 3D or volume DOEs without difficulties in mask-changing or mask-alignment.
A Fresnel zone plate is one form of a DOE. Fresnel zone plates are attractive because of their compactness and capability for high resolution while maintaining high efficiency. In the absence of losses and absorptions, an ideal diffractive zone plate can offer 100% diffraction efficiency provided that the zone plate correctly modulates phase. In practice, a quantized zone plate is used as an approximation of the perfect diffractive lens and its efficiency ranges from 10% to almost 100% depending on the number of quantization levels. Higher number of phase quantization levels provides higher efficiency, yet increases complication in fabrication. A 2-level Fresnel zone plate having a focal length f is constructed with a series of concentric zones whose radii are defined by
                              r          n                =                                                            n                ⁢                                                                  ⁢                λ                ⁢                                                                  ⁢                f                            +                                                (                                                            n                      ⁢                                                                                          ⁢                      λ                                        2                                    )                                2                                              ≈                                    n              ⁢                                                          ⁢              λ              ⁢                                                          ⁢              f                                                          (        1        )            where the integer n indicates the nth Fresnel zone and λ is the operating wavelength. The working principle of the Fresnel zone plate relies on the fact that the diffraction of light from alternating zones interferes constructively at the designed focal point. It is required that the alternating zones have different transmission properties (i.e., refractive index), and the incident light is monochromatic.
Studies of direct laser fabrication of Fresnel zone plates inside fused silica have been reported for both amplitude-type zone plates by utilizing scattering damage and phase-type zone plates by refractive index change induced by femtosecond laser pulses. However, all the previously studied zone plates suffered from low diffraction efficiency because of effects such as scattering from damaged regions, phase shift errors due to nonuniform index change inside fused silica, and planar fabrication. Attempts to fabricate multi-level phase zone plates were also reported, yet had difficulty eliminating the phase shift errors due to fabrication. See K. Yamada, W. Watanabe, Y. Li, K. Itoh, and J. Nishii, Opt. Lett. 29, 1846-1848 (2004).